This paper examines the revenue-smoothing hypothesis, which posits that an optimizing government will adjust both taxes and inflation to meet shocks to government spending. Our contribution is to examine this through the lens of a new methodology that relates both the first and second moments of inflation rates to central bank independence (CBI) measures. Unlike existing least-squares-based CBI papers, this study uses a maximum likelihood framework that facilitates the direct inclusion of CBI parameters in the residual covariance matrix. This new approach allows for a more intensive use of information contained in the CBI indexes and the estimates obtained are better reflective of CBI influences. Our results provide stronger evidence confirming the revenue-smoothing hypothesis, in particular for those countries with more independent central banks.